I am working in a circular building, with the following dimensions:
– height – 30m (approximated, 8+1 floors)
– diameter – 48m (measured on Google Maps)
– coordinates – 50.842519, 4.385583 (retrieved via Google Maps)
I was recently wondering how many days of sunlight the inner court of the building gets every year.

The elevation

Having the first two dimensions (height and length) I can easily calculate the minimum elevation, or the minimum angle made by the Sun and the horizon line to that a sun rays hits the court.
I used this tool even though calculating atan() and converting to degrees is also something that the Windows calculator can do:

So, it turns out that the minimum elevation (or Sun altitude) in order to have direct sunlight in the courtyard is 32 degrees.
PS – do not confuse the elevation with the azimuth:

The annual sun path

Now, we have the geographical coordinates and the minimum Sun elevation. All we need is the annual Sun path, which I got using this nice tool on sunearthtools.com:

This gave me a big Excel file with the days of 2016 (as rows) and time of the day in 15 minutes interval (as columns) in which all I had to do was:
– removing the azimuth columns (not useful)
– removing the columns when the Sun was not up (no Sun – no shadow 🙂 )
– highlighting the cells with elevation greater than 32.

The results are:
– the courtyard got 222 days of sunlight in 2016, from March 2nd (13:30) until October 10th.
– the earliest sun ray in a day was on 5th of June at 9:00
– the latest sun ray in a day was on 27th of June at 18:15
– most sunlight in a day: 8 hours 45 mins between June 5th and 27th
– least sunlight in a day: 30 mins on Mar 2nd and Oct 10th

Of course, since we’re talking about Brussels, the actual number of days of sunlight was probably only a small fraction of the total 222 🙂

The numbers do not change much from one year to another. I already added March 2nd 2017 at 13:30 in my calendar to see the first rays of sun in the inner courtyard. It would be like this (image from suncalc.org):

The comparison

To put these numbers into context, I compared with another famous circular building: the new Apple Campus in Cupertino.
Diameter: 360m (total 460m including the building)
Height: 20m (4 floors)
Coordinates: 37.335059, -122.008888
This leads to a minimum elevation 10 times smaller: 3.2 degrees instead of 32 in Brussels.
The results are clear, thanks to the large diameter of the building, the Cupertino campus court receives sunlight all around the year.
The most sunlight in a day: from 1st of June until 24th of July – 06:00 to 19:00
The least sunlight in a day: from 5th to 20th of December – only 8:00 to 16:00

Here is a comparison between the two locations (these are the Excel files zoomed out at 10% where the cells showing the elevation higher than the threshold are highlighted):

Resources

http://www.sunearthtools.com/dp/tools/pos_sun.php#annual
https://rechneronline.de/sehwinkel/shadow-casting.php
https://rechneronline.de/sehwinkel/shadow-length.php
http://www.suncalc.org/
http://www.photopills.com/articles/understanding-azimuth-and-elevation